A spline smoothing homotopy method for nonlinear programming problems with both inequality and equality constraints

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Mathematical Methods of Operations Research Pub Date : 2023-12-16 DOI:10.1007/s00186-023-00845-w

Li Dong, Zhengyong Zhou, Li Yang

引用次数: 0

Abstract

In this paper, we construct a new spline smoothing homotopy method for solving general nonlinear programming problems with a large number of complicated constraints. We transform the equality constraints into the inequality constraints by introducing two parameters. Subsequently, we use smooth spline functions to approximate the inequality constraints. The smooth spline functions involve only few inequality constraints. In other words, the method introduces an active set technique. Under some weaker conditions, we obtain the global convergence of the new spline smoothing homotopy method. We perform numerical tests to compare the new method to other methods, and the numerical results show that the new spline smoothing homotopy method is highly efficient.

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具有不等式和等式约束的非线性程序设计问题的样条平滑同调方法

本文构建了一种新的样条平滑同调方法，用于求解具有大量复杂约束的一般非线性程序问题。我们通过引入两个参数，将等式约束转化为不等式约束。随后，我们使用平滑样条函数来逼近不等式约束。平滑样条函数只涉及少数不等式约束。换句话说，该方法引入了主动集技术。在一些较弱的条件下，我们得到了新的样条平滑同调方法的全局收敛性。我们进行了数值测试，将新方法与其他方法进行了比较，数值结果表明新的样条平滑同调方法是高效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods of Operations Research 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience. All papers are refereed. The emphasis is on originality, quality, and importance.